JAZZED SACKS: Osi Umenyiora has reason to celebrate after the Giants gave the veteran defensive end a restructured deal for next season worth $7 million. Photo: AP

What Osi Umenyiora, his teammates, coaching staff and front office all wanted to see happen finally became a reality yesterday, when the formerly disgruntled defensive end agreed to a restructured contract that will keep him in Giants blue in 2012.

A source said no years were added to the contract and Umenyiora still will be a free agent after the season. But with the new contract, Umenyiora will make around $7 million, a significant raise over the scheduled $4.7 million.

“I’m just happy, I’m happy all that’s over with,” Umenyiora said. “It’s time to get back to work. It was definitely frustrating [not being on the field this spring], but hearing some of the things they said — whether it was Kiwi [Mathias Kiwanuka] or [Justin)] Tuck or JPP [Jason Pierre-Paul] or Antrel [Rolle] — hearing the way they supported me, it made me want to come back even more and be around them.

“Those guys really stepped up for me. I really appreciate it, and I’m happy to be here with them.”

Umenyiora and the Giants have been at odds seemingly since the moment he agreed to a seven-year, $41 million deal after the 2005 season. He tried to force a trade last summer and again this offseason while staying away from all team activities.

The news comes shortly after Umenyiora parted ways with longtime agent Tony Agnone, who told The Post earlier yesterday he was “stepping aside so the Giants can do the right thing and take care of [Umenyiora].”

That move sparked this new deal, one Umenyiora negotiated himself.

“I appreciate Osi’s patience and effort through this process,” general manager Jerry Reese said. “We talked it out, and it makes sense for everybody involved. We are very pleased, excited and looking forward to seeing No. 72 on the field at Monday’s OTA.”

A key component to the Giants winning their second Super Bowl in the past five seasons, Umenyiora, 30, received unanimous support from his teammates. In the past weeks, notables such as Tuck, Kiwanuka, Pierre-Paul and Rolle were adamant Umenyiora was stuck in a bad contract and deserved more money.

“This gives me peace of mind, definitely,” Umenyiora said. “We just resolved a situation. It really was affecting me in a bad way because I didn’t like all the negativity that was surrounding the whole situation. I couldn’t stand it, because if you know me, you know I’m not that type of person. I’m just happy all that is over with, and I’ll be there. I’ll play out this contract. I’ll play this year and I’ll play my heart out.”

Umenyiora battled knee and ankle injuries last season that limited him to nine regular-season games. He was dropped to a backup role after Pierre-Paul dominated in his absence.

But after returning from a high-ankle sprain in the season-ending, division-clinching win over the Cowboys, Umenyiora was a postseason force during the Giants’ Super Bowl run with 3 1/2 sacks in the four games. Overall, Umenyiora had 12 1/2 sacks in 13 games last season.

This is a win-win for the player and team. The Giants keep a feared pass rusher in their defensive-end rotation, and Umenyiora gets more money and a chance to play for a new contract in 2013 with the Giants or another team. Umenyiora, a second-round selection out of Troy State in 2003, has played all eight seasons of his career with the Giants.

Umenyiora said he was in top condition, according to the Giants, and will be at OTAs on Monday.